In an arithmetic progression, if the 1st term is x and the common difference is

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Question: In an arithmetic progression, if the 1st term is x and the common difference is 2, what is the expression for the 6th term?

Options:

Correct Answer: x + 10

Solution:

The 6th term is given by a + 5d. Here, it is x + 5*2 = x + 10.

In an arithmetic progression, if the 1st term is x and the common difference is 2, what is the expression for the 6th term?

In an arithmetic progression, if the 1st term is x and the common difference is 2, what is the expression for the 6th term?

Step 1: Identify the first term of the arithmetic progression, which is given as x.
Step 2: Identify the common difference, which is given as 2.
Step 3: Recall the formula for the nth term of an arithmetic progression, which is a + (n-1)d, where a is the first term, n is the term number, and d is the common difference.
Step 4: For the 6th term, set n = 6 in the formula. So, the 6th term is x + (6-1)*2.
Step 5: Simplify (6-1) to get 5. Now the expression becomes x + 5*2.
Step 6: Calculate 5*2, which equals 10. So, the expression is x + 10.

Arithmetic Progression (AP) – An arithmetic progression is a sequence of numbers in which the difference between consecutive terms is constant, known as the common difference.
Formula for nth term – The nth term of an arithmetic progression can be calculated using the formula: a + (n-1)d, where 'a' is the first term, 'd' is the common difference, and 'n' is the term number.